SALT LAKE CITY — The playoff race has hit its climax, but Amar’e Stoudemire needed what coach Mike Woodson called “a maintenance day’’ to rest his ailing knees Monday on the second night of back-to-back games.

After playing four games in six days, Stoudemire sat out the Knicks’ 92-83 win against the lowly Jazz in the finale of their Western swing as the team fights for its playoff life.

Woodson said Stoudemire was sore, but the Knicks power forward said this day off was planned before the trip began and he’s feeling “pretty good.’’

“I want to make sure I’m still strong for next month,’’ Stoudemire said of the rough April schedule as he sat in the locker room before the game eating a box of popcorn. “It’s not easy to sit out these type of games, but we got a tough schedule coming up next month against important teams and I want to make sure I’m full strength.’’

A familiar locker-room sight is Stoudemire placing his legs in supersized sleeves that resemble sleeping bags. He does it before each game to make sure his legs don’t swell up.

“It’s tough decision,’’ Stoudemire said of missing the game. “Not an easy decision to make.’’

Stoudemire entered the season believing he wouldn’t play both ends of back-to-backs, as per the medical staff’s order, but recently hasn’t abided by those restrictions.

His role has increased, starting 13 of the last 15 games he has played and was coming off a solid 15-point, 13-rebound performance in an 89-84 victory Sunday night over the Warriors. He hit two big free throws with 1:30 left to give the Knicks the lead for good and, earlier, put down a monster dunk midway through the fourth off an offensive rebound to help quell Golden State’s momentum.

“We got to protect him and get him ready for Brooklyn [Wednesday] when we get back home,’’ Woodson said. “Amar’e’s had a lot of bounce to his game. We got to keep him in a good place.’’

The Knicks have seven April games to close the season — all against playoff teams. Stoudemire said he expects to play all of them, since the final two comprise the only back-to-back.

In the small-ball alignment, Iman Shumpert was reinserted into the starting lineup at small forward. He had two. That hasn’t been an ideal situation for him, as sources say he believes he has gotten lost in the shuffle. Shumpert prefers coming off the bench.

Carmelo Anthony, who had 34 points in 39 minutes, had X-rays on his left hand after the Golden State game Sunday. The results were negative. He got hit on the hand by Andre Iguodala during the third quarter. … The Knicks are now 7-10 in second legs of back-to-backs.